For the exothermic reaction of $1 \ mol$ of $Zn$ dust with $1 \ mol$ of $H_2SO_4$ in a bomb calorimeter,the relationship between $\Delta U$ and $w$ is .....

$A$ mixture of $2 \ mol$ of carbon monoxide and $1 \ mol$ of oxygen is ignited in a closed vessel to form carbon dioxide. If $\Delta H$ is the enthalpy change and $\Delta U$ is the change in internal energy,then:

$C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$. The enthalpy change $(\Delta H)$ for the above reaction at $27^{\circ}C$ is $-1366.5 \text{ kJ mol}^{-1}$. Calculate the internal energy change $(\Delta U)$ for the same reaction at this temperature.

If $2 \ kJ$ of heat is released from the system and $6 \ kJ$ of work is done on the system,what is the internal energy change $(\Delta U)$ of the system?

During a process,a system absorbs $710 \ J$ of heat and increases its internal energy by $460 \ J$. What is the work performed by the system (in $J$)?

In a process,a system performs $238 \ J$ of work on its surroundings by absorbing $54 \ J$ of heat. What is the change in internal energy of the system during this operation (in $J$)?